Abstract: Computer-aided verification provides effective means of analyzing the
security of cryptographic primitives. However, it has remained a
challenge to achieve fully automated analyses yielding guarantees that
hold against computational (rather than symbolic) attacks. This paper
meets this challenge for public-key encryption schemes built from
trapdoor permutations and hash functions. Using a novel combination of
techniques from computational and symbolic cryptography, we present
proof systems for analyzing the chosen-plaintext and chosen-ciphertext
security of such schemes in the random oracle model. Building on these
proof systems, we develop a toolset that bundles together fully
automated proof and attack finding algorithms. We use this toolset to
build a comprehensive database of encryption schemes that records
attacks against insecure schemes, and proofs with concrete bounds for
secure ones.